where \(\delta _{nl}\)  is the evolved density contrast and \(T_{\gamma }\)  is the CMB temperature. The effect of peculiar velocities is ignored in the above expression because they are very small in magnitude compared to the expansion rate of the universe at the redshifts and scales of interest [1]}. Here, \(T_S\)  is the spin temperature which describes the relative population of the hyperfine levels and is given by the Boltzmann distribution, \(n_{1}/n_{0}=3~\) exp \((-T_{*}/T_{S})\) . For our study, we work in the post heating regime where \(T_S \gg T_{\gamma }\) . This assumption is valid during most of the EoR [2]} as the IGM would have heated by X-ray sources prior to ionization [3]}, [4]} and \(T_S\)  would have completely coupled to the gas kinetic temperature of the IGM. Therefore from eq. (REF ) the morphology of \(\delta T_b\)  would depend solely upon the morphology of \(\delta _{nl}\)  and \(x_{HI}\) .
